PHYSICS 5710 and 3220 ADVANCED CLASSICAL MECHANICS
FALL 2017 SECTION:001 MoWeFr 8:00 -8:50 a.m. PHYS 112
Recitation We 2-2:50 p.m. PHYS 116
Instructor: Dr. Arkadii Krokhin GAB 525J phone: (940)565-3968,
e-mail:
Office hours: Mo 10-11 a.m., or by appointment
Main textbook: L.D. Landau and E.M. Lifshitz, Mechanics, any edition.
Course Description: This is an advanced course of Classical Mechanics based on Lagrangian and Hamiltonian variational principles. It is intended for graduates (and advanced undergraduates) in physics and related fields. Completion of the undergraduate courses in Mechanics, Electricity and Magnetism, and Calculus is required. The primary goal of the course is to prepare students for further study of the graduate courses of Electrodynamics, Quantum Mechanics, and Statistical Physics.
Course content
I. Introduction to calculus of variations. Calculus of variations in physics. Fermat principle in optics. Brachistochrone problem.
II. The Equations of Motion
1. The principle of least action.
2. Galileo’s relativity principle.
3. The Lagrangian of a particle and of a system of particles.
III. Conservation Laws
1. Time-independent Lagrangian, conservation of energy.
2. Coordinate-independent Lagrangian, conservation of linear and angular momentum.
3. Mechanical similarity.
IV. Integration of the equations of Motions
1. Motion in one dimension.
2. Determination of the potential energy from the period of oscillations.
3. The reduced mass.
4. Motion in a central field.
5. Kepler’s problem.
V. Mechanical Collisions
1. Disintegration of particles.
2. Elastic collisions.
3. Scattering.
4. Rutherford’s formula.
5. Small-angle scattering.
VI. Small Oscillations
1. Free oscillations in one dimension.
2. Forced oscillations.
3. Oscillations of a system with many degrees of freedom.
4. Damped oscillations.
5. Forced oscillations under friction.
6. Parametric resonance.
7. Motion in a rapidly oscillating field. Kapitza’s pendulum.
VII. The Canonical Equations
1. Hamilton’s equations.
2. Poisson brackets.
3. The action as a function of coordinates.
4. Canonical transformations.
5. The Hamilton-Jacobi equation.
6. Separation of the variables.
7. Adiabatic invariants.
There will be 3 tests during the semester and the final comprehensive exam.
GRADING: Tests: 3x20% , Final:25%, Homework and activity in the class:15%.
Attendance: is not required but highly recommended. Tests are mandatory.
The University of North Texas makes reasonable academic accommodation for students with disabilities. Students seeking reasonable accommodation must first register with the Office of Disability Accommodation (ODA) to verify their eligibility. If a disability is verified, the ODA will provide you with a reasonable accommodation letter to be delivered to faculty to begin a private discussion regarding your specific needs in a course. You may request reasonable accommodations at any time, however, ODA notices of reasonable accommodation should be provided as early as possible in the semester to avoid any delay in implementation. Note that students must obtain a new letter of reasonable accommodation for every semester and must meet with each faculty member prior to implementation in each class. Students are strongly encouraged to deliver letters of reasonable accommodation during faculty office hours or by appointment. Faculty members have the authority to ask students to discuss such letters during their designated office hours to protect the privacy of the student. For additional information see the Office of Disability Accommodation website at http://www.unt.edu/oda. You may also contact them by phone at 940.565.4323.
UNT’s policy on Academic Dishonesty can be found at: http://www.vpaa.unt.edu/academic-integrity.htm
Drop information is available in the schedule of classes at: http://registrar.unt.edu/registration/schedule-of-classes
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Near the end of the Fall 2017 semester you will receive an email on from "UNT SPOT Course Evaluations via IASystem Notification" () with the survey link. Please look for the email in your UNT email inbox. Simply click on the link and complete your survey.
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